© 2015 American Physical Society. In a combined experimental and theoretical study, we investigate the properties of Sr2Ir1-xRhxO4. From the branching ratios of the L-edge isotropic x-ray absorption spectra, we determine that the spin-orbit coupling is remarkably independent of x for both iridium and rhodium sites. DFT+U calculations show that the doping is close to isoelectronic and introduces impurity bands of predominantly rhodium character close to the lower Hubbard band. Overlap of these two bands leads to metallic behavior. Since the low-energy states for x<0.5 have predominantly jeff=12 character, we suggest that the electronic properties of this material can be described by an inhomogeneous Hubbard model, where the on-site energies change due to local variations in the spin-orbit interaction strength combined with additional changes in binding energy.